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A241668 Sum of iterates of A241663 up to and including either 0 or 1.

%I A241668 #16 Oct 01 2018 21:06:59
%S A241668 1,0,0,0,1,0,3,0,0,0,10,0,9,0,0,0,22,0,15,0,0,0,34,0,6,0,0,0,31,0,27,
%T A241668 0,0,0,3,0,33,0,0,0,70,0,39,0,0,0,82,0,21,0,0,0,70,0,10,0,0,0,65,0,57,
%U A241668 0,0,0,9,0,63,0,0,0,130,0,69,0,0,0,21,0,75,0
%N A241668 Sum of iterates of A241663 up to and including either 0 or 1.
%C A241668 This sequence is similar to the totient summatory function A092693, but uses the Schemmel totient function A241663 instead of the phi function.
%H A241668 Antti Karttunen, <a href="/A241668/b241668.txt">Table of n, a(n) for n = 1..65537</a>
%H A241668 C. Defant, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Defant/defant5.html">On Arithmetic Functions Related to Iterates of the Schemmel Totient Functions</a>, J. Int. Seq. 18 (2015) # 15.2.1
%e A241668 A241663(11)=7, A241663(7)=3, A241663(3)=0, so a(11)=7+3+0=10.
%e A241668 A241663(9)=0, so a(9)=0.
%t A241668 L[n_, m_] :=
%t A241668 If[Min[Select[Divisors[n], PrimeQ]] <= m, 0,
%t A241668   n*Times @@ (1 - m/(Select[Divisors[n], PrimeQ]))]
%t A241668 a[0]:=0
%t A241668 a[5]:=1
%t A241668 a[n_]:=L[n, 4]+a[L[n, 4]]
%o A241668 (PARI)
%o A241668 A241663(n) = {my(f = factor(n)); prod(i=1, #f~, if ((f[i, 1] == 2) || (f[i, 1] == 3), 0, f[i, 1]^(f[i, 2]-1)*(f[i, 1]-4))); } \\ From A241663
%o A241668 A241668(n) = { my(s=(1==n)); while(n>1, n = A241663(n); s += n); (s); }; \\ _Antti Karttunen_, Oct 01 2018
%Y A241668 Cf. A092693, A241663, A241665.
%K A241668 nonn
%O A241668 1,7
%A A241668 _Colin Defant_, Apr 26 2014